Qryrnnnr"
_f
16l?4rr
ir4ccttr,4l- €'4x'rsr'*' u> nn-p"'{a) "na'l 0r
*
i'trtrte-/52,'zc'ry
s,r;;...,-1.ftlrna&t,tg
f not sg'e'l;c tu uYi / 'n unybe I
Aft! g'{1t&t-iin,
w'Y|
*P#:{:Experiment
tt ;s *n{*";;
Meazu,ues
the BoltzmannConstant7
phr*:ey, rcn*(of
;-&re I f,tvttn
A" t+,mp(de Stuffn<r 't* be l& titk uf e sara&,T)z lafn
November15, 2013
"l:il"u'f
'
k*'
v"({vza?
be''r''u*'ffi'uf":l':::+vn'd
i'rehar
' '|-
on/t1 U';'lftS(S.z
By using a diode we were uUf.ftp construct a circuit from which we measureddifierent voltages. Flom these measurements we were able io
he value of the Boltzmann
constant
".Ul* shocklerlp*e
"rffirl
lnilrt lesbt& ?
thtt)4
Theory
0c/,r tqhn g,t ?
,/
In this exlerimelwe measuredthe valueof the Boltzmann
^rrby
$n
ideal diodeequation11]
|
,./a0od
I : Io(""v/ktT- r). .z
,
using the Shockley
(i)
\"/ Jaact
,
This a.llowedus to relate the current through the diode to the voltage acrosst\yi{ode.
In
i. *n" current though the diode, 1o is the reversesaturation current, e is the
this equatiorfi
-v
fundamental element of cha,rge, I/ is the voltage across lhe diode,, 7 is
i the temperature inside
.//'"r/
7{tne
diode,andksis the Boltzmannff.nstant
,Y , .
Ae iq6{nu'w"'(
' " ' ' r v ' \ J t!{r'd
tuLw
c'n/
vuL4"\
cculil
krs
r-tt
L'l
'rf
AVOfL*t*utn
A (,Uoltttrg/;nftorl,*,y'tnn
' ut qv tnJde
'lS/,llfu
).s €,xt'rtulJ
hZ ind,dee/ " f*lotiyut;^
m*ti',nt1n ouutor
fttttttlr'C/.h\
Cuu{c(t'L
Method
Y( Stttrcl' Pa pt"e'rsand Mat eri{2,v"
\,/
8tfueiltnpntriay
'
-,t
,.i
/ .'
r/" fuh,G,
,rJ^
( tlttvt/ewvT
w*re
we
rec,,(q il&{rt
{ot re?41
il,*/,y
i
*
//4/)"'Y-(e""( "74y rcc4
rnaft#ads"
Lv)tA /rtq//\r'tt6''/>'
t'vtfA
JWe measured the voltage at two different points in the circuit (Fig. 1) using a Hewlett Packard
an uncertaintvof + 0.005V.By meaMult'i,meter
972A which gaveour voltagemeasurements
6il;n
//eA*'unpno,,u)
o4ingnno*4ilt is ''P';tY u
ill (wt'c\;s#wtrutil
yx6^.t,i*674ffi(r{rmny4sfi5 cn t|'p yr"Jh a",t ex/{a)nttp;f@,
Ya /t^aW
16gt",rS " I7e4
hqre rliyera"1
I {t(cisiut.
(, Slvtl"lrt |cte
/*a
Swi+c
*/r(', fu
r"pxw{4 s
u,tdtr<?aa/,
figu'e.
ilrePlaa'd
Fywe cef+,"s
-t5 ld
$lena
dtb,'(ed '. )u"eltt yu{€
k'ufe lx&v'rL(6
wu{t( b4
.It t"t"ta(
reaalert t*fo
ffi;{rq'
*t *;'fr , be4
rud fl,,tres*>,Atvrytlws
ft'f4 t
i, ,*,t4+ wA'V
fut,d,;,3'
;&tJ*
{A}1;
Atran!,rfu1>
Et{fi.3Si{l
ts rfiet*r
pin
ffi-l
ts r*€tsr
rtrta d iocfu-
Y
P^rtrf it u'ts (,;[b; ;dul e1/t^
avtaxt
;( )rt 2lahruTtbn
ezpLiln
(,.1d;1in &w
fi,urt*^
lowcan
suring ihe voltdg6 at two points we were able to indirectly measurethe voltaqe
1;'
i c'-+1
\dAr.,'. a,nd
crrrrent through
throush the
the tr9(tot
trail#tor.
the current
andthe
ttuffitor,
,";
H t
4tvr(\
/
CtVl / &LYrD
./\
mdirectly
. t
measured the voltage across the @i"€q[ya
--;V
-:---
,r
tk fihni,su(
,t'
'/\
/r((a*a(
/'
ryrdss the
*u4,
4 t';(A
Bv measurinethe voltase utYoint f'lw"
"5lu*u%
dW
-'
jwittr respect to groundby-bhranrsee'f-
?rfi nt ; t c@t t1
i , , vn
-vt. "'i )'r|*rr",i' ,,,,/r';i' vlrf&
t/
,r 't.,
,,I t ?zttv Tl
l::" Royr&Htk ,/io/,t7furoi,t r. -/^
Ot'Lrre&"
fltS[ fll (ntvT
/ "
':
, s b/4 f 'kt*4 of l o''^t A
had to usea LF356 op-ampcurrentTo measuretne@d6'W.frrough the transistor uli{*
/.
e 7,
voltageconverterbecausethis curryllli,trmall. This madeit possibleto havea readablevoltage. WA-A{
By measuringthe voltageat point B,Vs,we wereableto indirectlymeasurethe currentthrough ,:O::
::'*n*,
:f^*c'szamqc4,
by using
thetransistor
1r,
uYrtrc{-
t"$i{yA
V:
fi
,^,pryc,sc*Xi'"
o''"f':'u:""ii'*'t
90"1
of the 1 ko pot. L{lke*;5 ,rpr*,#
ffi*{<c.ge alteredtheresistance
We also assumed that the voltage across the diode will make
"evlksT
)>
1 so we were able to
-t":
approximatethe current through the diode t":?
,
I x loeev/keT .
'',
2
:t;ry#,
tk
/,A ffg^*
Vo(.{c,gZtan,^d*f
*/,e Smao/'&tt4.e,"t.e*n
h*,n €t,s(r{l)ra
preers€lq
w,frhovtbe/nq/,sAriU
ti
o{ e&tf&{ 4 *At-neattrer',d4
T
'
ou.{,
.
;g;;i$nt{- i i4 ,-11,
e
L'A/Fi 1'' t)wtt/1 ,
jr;Lw(, i=
4"ol
y
;
"+ 7 /,tco/4rn
/.rtr'L J
t
L.-) t,{-r
;.
''-f h",vvp,'tt\ .)
luWu rt'e(trt li,tv Avr.Tzqrt'ttrl
We are able to assumethis by starting out measuredvoltageat point A at approximately-0.6V.
From this we can seethat the current will be on the ora", of b)@Junicn
make this approximation valid. F}om this we obtained m#
"
thevottage
v:
LnI:#-tfgr".
rnship betweenl6yI and
r\ttn_>ltrj,,I .
[-rl,r,'ir.rr,
(,t),'t'-.,
,,1i,
,r\""4{4Yiui
' , _ . . , , " "'{oi'trutari1p'
,' _+.,
')'^F'"';'9'"')'.'.'
vv6ri
k615,"or-g/,,"(,,"t:":K:!!:f":i;J,L:l
;-":,;
e'-- 1\\..
is large enoughto
/Ai [
,ietz.W,\,t";r(+
1 ;, , , , - 6 t ' E -
1,r=---1rii"
this'
'
/p,r- ki:
-!/;), ,.r,:.k.1
We measuredthe resistorRl to be g.gg7+0.002 kfl usinga Stanford,ReaserchSR 7115meter.
1V,tk,/; {,{{/s:;t ,t(;i{rrr,.z-,
,/
PB-503"Protoboard"C'ircu'it
We createdthe circuit ona GlobalSpeci,alti,es
Boardy![&,gna]_y'lit:k-,/*,q
t/r-t
Generator and used BNC Coaci,alCables to connect the multimeter's to the Protoboard. We
LrlL,tltr*,
. ^ - * 't-
rgnoredthe resistancean4 c4ficrtance of the BNC cablgr"cables.During the experimentwe
v,'
v
Ur'
tuh,r,h p1,iyg
-Luh.,_/r.i)r,,rt
^
,:;i.,-ti,,r
,r4Vq"'
| :
,ttlXr,tiun(i1
used a 2NSg04 transistor instead of a diode and assumedthE transiAtoi''would act as a perfect
F'z
tl'r;,
(d:/''
-._--i
-_--j
-l/,u
1rr.t,.:,/,:5.,1
would stay under f .),.,;,, la,; ;.v-1,of thesevoltagesw to n{}ne
W**#E-u#*"ururements
l/
tvt'lpf y',ft':1ri
'
t
rl ft;a l-*,
the saturationvoltage.
,!-t l,' ,,/ t-t -'"
i:;gt Ltyt )'( {v|'i'1/v1v' 7:f'4La7ir
-''
/
We made the assumptionthat the temperatureinsideof the transistorwill be approximately
diode. We
: I i n'''
fir1rilV'r.
J(
equalto room temperaturf],rri"t we havemeasured
ro u"d+ - 0.5 K usinga mercuryther,),"'l/t'^
'url
U
f,u
d.. . , . .!l ,.,t+,,
/
trbZ
i
;
'
r
!
',1t,''''|u\t,r1'l'.".mometer.ThevoItag.ru'"ntheop_ampwaSmeaSu,"t}+.os+0.005Vand.ftlo,"+ryyLin./
,ti,,,,\
L,i t*'J
flrt
w
tnevoltage
gi1t1ial5fffiand
" ; + 0,005v. Wealso * i), i,' l,/ik:I\
to be -14.94
thecircuitwasmeasur.ed
nl+ry^ui, assumedtheelementoffundamentalchargeetobeexactlyl.64xl0-1eCl3].
6iA
rto-'k,
:,if.= ]Co(-
t
._,u,ti,5tt4 .:
,
t"t'(l'u"t'rtr:/.*
t,LLpL,
w!;,;t;:'y,{:':,':,{;,,#,
',,''*"?,;': ni'li'i''
r&ll/Resurts
,),:,"1)"n
,-".':,:,:;;i!;J;,"-),i'
:;o!r';
i^":,'
-. *:* ":""-,
'"
-:'" ";","" tt- *-,
":- -:
.. ll
:
hrt'
Jt ;f
-*
f
f
-------ll*\
y. ^.
L
:",,
:" /l(t".u,
',/
we expectedin Eqn. 5. The SravI;fT\8. 2 is a semi-logplot of the current through the diode I
._
='' dt'zt / /rr,
versusthe voltageacrosstrre {$r.d. We wereable to plot the data in Matlab using the program
Y
Flom the measurement,-JdL,"*" fopnd that the relationshipbetween tgql and,Vvrur'lin"ui u,
i, , , ,
5t
,j(
T'l
,
{.t,i.( ulQ
\/ '
Boltzmann co\gbdnt. The/reducel ch'i-squaredof our measurementsis 874.88. Our measured
Y:
) j':
- ::- 't n(6n ?
- ll'L;
wtwlt"n"{ \''c
lYtwt
Lt
c'Botrr*unn
;'> /(;r
i)< 10-'J J/K. The known
r.r,o''rrvalue
rr.ll".
constant,kB-"*., wasmeasured
t" b"(;;1+'0.,i6)"lo3?'liN"i'rr"
(i,ttlo,a6)
(
X,iit
_
I
."i/'''l)
1-**-**e
'ilitakt
qrh'/'tt"7t:'/
'
61Ll"pd!1
We;'"e
r*
al
tv':"s
f,,,d
lt-ls
tftte
f-ti:t/7
L'i*l'
,vtt-,.wo,rh
-!r^'Jrtttt'l;;';:
t }'4k',r,'at' i t"'{t"@t*'( Ls
i76tu{t't
d",tfui
i,,*o
* O-, ^:,,!*i '
hl fi$":"l/" '
trf't5 't4L*"e'1r'|a''tat
z
,r"'kv
1,,*r,{t,i,,, ,'i
t),;'.ult
4k:
i )
*iln
$N.t- #xp l$r,,t
alu-t
llat h)
,re/t ahz
tlna( 4 t*
is rzez-.ta
,i
I Figure 2: Semi-logplot of Current versusVol
41.103x+-34.1056
ds,F.1_988q
delb= 1^2847
-*
of the Boltzmann constantis ,be:l3aT1O-23 J lKlS]. Although the value for the known value
\)gtnute
ev are both on the same
^
v{uY of the Boltzmann constant does not lav within our
*,tei,in
discrepancyis most likely due to only havetwo significantfiguresfor
ggggt$acsitudg-This
,.4n1,r,&':'4
the voltagesmeasuredwhich causedus to have multiple data points for one uortage./-i''it;''''''
Su r ' * '
., , I
i''"dyp-
'?
vt,hi;tnr'lhyq ci*4* 1"t)'4 ?
C [. (tle- tl*lnhrn
'= ()' i 7 7 /]1d/t4
t rlrt J'ii lpa''t (rnuf
tae,ffrd^*)
t;'
y{,;*lm5l,rJ,,?t:tw14 P-t'
^/'.L
)rn,
=
b"l'
+ut ?l"t^
alnw"Wl
f i"
v( tL's95"'if't'*C1
] a A'bv )
fts)trrnd
"',':^t,'!',|)",iff; ,y.srt*/
o)
/)1ce{lj, f/'it
+,01
+,0t
)
d
(itr'!l),'eort/'
av
"s
FL*'
rew
4f
-tu ni rtt€6iar*ti
{y.7,;,rT,#'"/)'n:^"::'
w^ro'ut:r'r
hvyt,rtr!
i+ .')nrrtcn.rt
r"ur",iclr
,b.,s.tl|;' p*}'&o^*!,1-e,|eo(,t*.(
D,,t
('A' "n
,J4
tiln /.|4
{,/!J
fvf}€Je,{ *^4
v$o;'eyn(-tco-'{
\
pt',t
*nu,*;4 r! tL |i#.,:J
, :* C4;sc'efwg
l,*,ro
*9
tLrtbtt'<
awfudvr,
ryY=7/0,
H
,it
uihdi,,gSt,m,n*eo:.
bo"t'tr
whicAis n*
is uval
hotcl
, 7looy r\;stnPa^ry
tl"an"'0\-Uda,ei'Y
W!!'9:''
/
ydw nzt4 *
la hul 4 ef
W
b(a,r a/^/^<
),,yuotvd
,/ *V w/.,p-tfur<2, onaf ,,uh"r{ ?a.nk
References
sr'^&" Sle! pos)*'*e. ,: /n-v
+- ,-f^"(t''"e
con rLs2ayt^
[1] A. Sedra,K. Smith: MicroelectronicCircuits. 4th ed. New York, New York: Oxford, 1998.
p132-134
\
'/ /
[2] J. Lockhart, W. Man:
{t n,-at;y
Pur(
Advanced Lab l- Manual and S-upplementary information.
Version
F13, San Flancisco,CA: San FlanciscoState University 2013.p76-82
[3] R. Eisberg,R. Resnick: Quantum Physicsof Atoms, Molecules,Solids,Nuclei, and Particles,2nd ed. United State of America: John Wiley & Sons,Inc. 1985.
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ca'4 ce(